A critically tapered fold-and-thrust belt or submarine accretionary wedge is one that is on the verge of Coulomb failure everywhere, including its base where frictional sliding along a decollement is assumed to be occurring. Cohesion within a wedge can add significantly to the overall strength near the toe; the effect of this is to decrease the near-toe taper, leading to a critical topographic profile that is concave upward if the decollement is planar. We obtain an approximate self-consistent solution for the state of stress within a thin-skinned cohesive critical Coulomb wedge, and determine the relationship between the wedge taper and its strength and basal friction. The theory is then applied to the presently deforming fold-and-thrust belt of western Taiwan. Fitting of theoretical critical wedge shapes to topographic profiles and measurements of the step-up angles of thrust faults from the basal decollement are used to constrain the Taiwan wedge strength parameters. An attractive assertion fully consistent with all the observations is that the mechanics of fold-and-thrust belts and accretionary wedges is governed by normal frictional and fracture strengths of rocks measured in the laboratory. In particular, if Byerlee's law µb = 0.85 is adopted as the coefficient of sliding friction on the base, we find a coefficient of internal friction µ = 0.9-1.0 in the wedge and a wedge cohesion So = 5-20 MPa. Other solutions having strengths and ambient stresses up to 4 times lower than this can also, however, satisfy the data.